How do you solve the triangle ABC given a=7, B=60, c=9?

1 Answer
Jan 10, 2017

Answer:

Use the Law of Cosines to find the length of side b.
Use the Law of Sines to find A.
The sum is 180 for C.

Explanation:

Use the Law of Cosines to find the length of side b.

#b^2 = a^2 + c^2 - 2(a)(c)cos(B)#

Substitute, 7 for a, 9 for c, and 60 for B:

#b^2 = 7^2 + 9^2 - 2(7)(9)cos(60)#

#b^2 = 67#

#b = sqrt67#

Use the Law of Sines to find A.

#Sin(A)/a = sin(B)/b#

#A = sin^-1(a/bsin(B))#

Substitute, 7 for a, #sqrt67# for b, and 60 for B:

#A = sin^-1(7/sqrt67sin(60))#

#A ~~ 48^@ #

The sum of the angles is equal to #180^@#:

#180^@ = A + B + C#

Solve for C:

#C = 180^@ -48 - 60#

#C ~~ 72^@#